[Une méthode de projection superconvergente pour les équations d'opérateurs nonlinéaires compacts]
Nous proposons une méthode, basée sur une projection, pour approcher les points fixes localement uniques d'un opérateur compact. Cette méthode présente un avantage par rapport aux méthodes de Galerkin et de Galerkin itérée étudiées par K.E. Atkinson and F.A. Potra : on n'a pas besoin de conditions supplémentaires pour obtenir la superconvergence de la solution approchée vers la solution exacte.
We propose a method based on projections for approximating fixed points of a compact nonlinear operator. Under the same assumptions as in the Galerkin method, the proposed solution is shown to converge faster than the Galerkin solution.
Accepté le :
Publié le :
Laurence Grammont 1 ; Rekha Kulkarni 2
@article{CRMATH_2006__342_3_215_0, author = {Laurence Grammont and Rekha Kulkarni}, title = {A superconvergent projection method for nonlinear compact operator equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {215--218}, publisher = {Elsevier}, volume = {342}, number = {3}, year = {2006}, doi = {10.1016/j.crma.2005.11.011}, language = {en}, }
TY - JOUR AU - Laurence Grammont AU - Rekha Kulkarni TI - A superconvergent projection method for nonlinear compact operator equations JO - Comptes Rendus. Mathématique PY - 2006 SP - 215 EP - 218 VL - 342 IS - 3 PB - Elsevier DO - 10.1016/j.crma.2005.11.011 LA - en ID - CRMATH_2006__342_3_215_0 ER -
Laurence Grammont; Rekha Kulkarni. A superconvergent projection method for nonlinear compact operator equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 215-218. doi : 10.1016/j.crma.2005.11.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.011/
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